This is found if we set z = 1/2 in the reflection or duplication formulas. If we simply make the substitutionu = √t in the integral definition of the gamma function, we get a Gaussian integral. In general, for non-negative integer values of n we have:

Bernhard Riemann found a relation between these two functions. This was in 1859 paper "Über die Anzahl der Primzahlen unter einer gegebenen Grösse" ("On the Number of Prime Numbers less than a Given Quantity")